1. Field of the Invention
The present invention relates to a method and an apparatus for measuring the amount of a gas adsorbed on a solid material.
2. Description of Related Art
For advantageous use of solid materials such as powdery materials, adsorbents and films, it is important to obtain information on the specific surface area and pore size distribution of such a solid material. To obtain such information, it is necessary to prepare an adsorption isotherm by measuring gas adsorption on the solid material while maintaining the solid material at a constant temperature.
For example, a volumetric gas adsorption measuring apparatus as shown in FIG. 4 is employed for the measurement of the gas adsorption on the solid material. As shown, the volumetric gas adsorption measuring apparatus 50 includes: a manifold 51 maintained at a predetermined temperature (T) and having a known geometric volume (Vs); a sample cell 52 which contains a solid sample A and is connected to the manifold 51 via a valve 54; and a constant temperature bath 53 which contains a cryogenic coolant such as liquid nitrogen. A gas inlet/outlet line is connected to the manifold 51 via a valve 55, and a sample retaining portion 52a of the sample cell 52 is immersed in the cryogenic coolant contained in the constant temperature bath 53 for maintaining the solid sample A at a cryogenic temperature.
With the use of the volumetric gas adsorption measuring apparatus 50, the amount of a gas adsorbed on the solid sample A is measured in the following manner. First, the manifold 51 and the sample cell 52 are evacuated with the valves 54 and 55 being open. Then, the gas is fed into the manifold 51 with the valve 54 being closed, and the valve 55 is closed. At this time point, a gas pressure (Pi) is measured. Subsequently, the valve 54 is opened, and the gas is introduced from the manifold 51 into the sample cell 52 thereby to be adsorbed on the solid sample A within the sample cell 52. When an adsorption equilibrium is reached, a gas pressure (Pe) is measured.
Provided that the gas fed into the manifold 51 is an ideal gas, the following expression is satisfied:
PiVs=n1RT
Pe(Vs+Vd)=n2RT
wherein Vd is a dead volume of the sample cell 52 (i.e., the volume of the sample cell 52 excluding the volume of the solid sample A on the assumption that the gas introduced into the sample cell 52 is maintained at the same temperature as in the manifold 51), n1 is the number of moles of the gas fed into the manifold 51, n2 is the number of moles of the gas after the adsorption, and R is the gas constant. Therefore, the amount (N) of the gas adsorbed on the solid sample A is expressed by:
N=n1xe2x88x92n2=[(Pixe2x88x92Pe)Vsxe2x88x92PeVd]/RT
Therefore, the dead volume (Vd) of the sample cell 52 is generally determined prior to the measurement of the gas adsorption on the solid sample A. More specifically, the manifold 51 and the sample cell 52 are evacuated with the valves 54 and 55 being open. Thereafter, a non-adsorbable gas which is not adsorbed on the solid sample A is fed into the manifold 51 with the valve 54 being closed, and then the valve 55 is closed. At this time point, a gas pressure (P1) is measured. Subsequently, the valve 54 is opened to introduce the non-adsorbable gas from the manifold 51 into the sample cell 52 retaining the solid sample A. At this time point, a gas pressure (P2) is measured.
Provided that the non-adsorbable gas fed into the manifold 51 is an ideal gas, the following expression is satisfied:
P1Vs=nRT
P2 (Vs+Vd)=nRT
wherein n is the number of moles of the non-adsorbable gas fed into the manifold 51, and R is the gas constant. Therefore, the dead volume (Vd) of the sample cell 52 is expressed by:
Vd=(P1xe2x88x92P2)Vs/P2
Thus, the measurement of the gas adsorption on the solid sample A can be achieved by preliminarily determining the dead volume (Vd) of the sample cell 52 retaining the solid sample A. Since the aforesaid adsorption isotherm indicates a change in the gas adsorption (N) on the solid sample A observed when the ratio Pe/Ps of the gas pressure (Pe) in adsorption equilibrium to the saturation vapor pressure (Ps) of the adsorbable gas is changed from zero to one, the aforesaid process is repeatedly performed for the preparation of the adsorption isotherm. That is, the amounts (N) of the gas adsorbed on the solid sample A are determined while the gas pressure (Pe) in adsorption equilibrium is progressively changed. Therefore, the measurement of the adsorbed gas amounts (N) for the preparation of the adsorption isotherm is a time-consuming operation.
Further, the cryogenic coolant such as liquid nitrogen contained in the constant temperature bath 53 is highly evaporative, so that the surface level of the cryogenic coolant is remarkably lowered with time. Even if the sample retaining portion 52a is completely submerged in the cryogenic coolant, the environment (temperature) of the sample cell 52 above the surface level of the cryogenic coolant constantly changes as the surface level of the cryogenic coolant is lowered. As a result, the dead volume (Vd) of the sample cell 52 is changed.
For accurate determination of the gas adsorption on the solid sample A, the dead volume (Vd) of the sample cell 52 should be determined every time the adsorbed gas amount (N) is to be measured. Thus, the preparation of the adsorption isotherm is a troublesome operation.
Therefore, consideration is given to the conventional volumetric gas adsorption measuring apparatus 50 for constantly maintaining the surface level of the cryogenic coolant with respect to the sample cell 52 immersed in the cryogenic coolant, so that the dead volume (Vd) of the sample cell 52 initially determined can be employed for the measurement of the gas adsorption to be performed later. This eliminates the need for determining the dead volume (Vd) of the sample cell 52 every time the amount (N) of the gas adsorbed on the solid sample A is measured.
A common approach is to provide a lift mechanism for moving up and down the constant temperature bath 53 so that the surface level of the cryogenic coolant is constantly kept at a predetermined height with respect to the sample cell 52, or to provide a coolant supplying mechanism for replenishing the constant temperature bath 53 with the cryogenic coolant so as to prevent the change in the surface level of the cryogenic coolant within the constant temperature bath 53. In either case, the change in the surface level of the cryogenic coolant should be detected by means of a temperature sensor or the like for actuation of the lift mechanism or the coolant supplying mechanism. Therefore, an expensive temperature sensor should be employed for accurate detection of an abrupt temperature change, thereby increasing the costs. Further, the accuracy of the temperature sensor may be reduced by corrosion or frosting of a temperature sensing probe of the sensor.
Another conceivable approach is to provide a cryogenic coolant outlet at a predetermined height of the constant temperature bath 53 so that the surface level of the cryogenic coolant within the constant temperature bath 53 is kept constant by continuously supplying the cryogenic coolant to the constant temperature bath 53 and constantly letting out the cryogenic coolant from the outlet of the constant temperature bath 53. This approach requires a cryogenic coolant circulating mechanism, thereby complicating the construction of the overall apparatus.
Rather than maintaining the surface level of the cryogenic coolant at the constant level, further another conceivable approach is to cover the sample cell 52 to a predetermined height with a cylindrical jacket of a porous material (e.g., ceramic) which can suck up the cryogenic coolant from a lower portion thereof immersed in the cryogenic coolant by capillary action or to cover the sample cell 52 to a predetermined height with a cylindrical jacket of a highly heat-conductive metal material having a lower portion immersed in the cryogenic coolant, whereby the environment of the sample cell 52 is maintained in a generally constant state. However, this approach often fails to assuredly maintain the environment of the sample cell 52 in the constant state if the change in the surface level of the cryogenic coolant increases.
Further, the jacket of the porous material is cooled to a cryogenic temperature when sucking up the cryogenic coolant. Therefore, the jacket adsorbs moisture in air immediately after being detached from the sample cell upon completion of the measurement of the gas adsorption. It is cumbersome to dry the jacket before the jacket is reused.
It is therefore an object of the present invention to provide a method and an apparatus for measuring gas adsorption, which ensure easy and accurate measurement of the amount of a gas adsorbed on a solid material without the need for maintaining the environment of a sample cell in a constant state.
In accordance with the present invention to achieve the aforesaid object, there is provided a method for measuring an amount of a gas adsorbed on a solid sample, the method comprising: a preparatory process which comprises the steps of: preliminarily determining a dead volume of a reference cell for determination of a dead volume of a sample cell which retains the solid sample and, at this time point, filling and confining the gas in the reference cell; measuring an initial dead volume of the sample cell and an initial internal gas pressure of the reference cell with the sample cell and the reference cell being immersed in a cryogenic coolant contained in a constant temperature bath; and calculating an initial dead volume of the reference cell at a time point of the measurement of the initial dead volume of the sample cell on the basis of the initial internal gas pressure of the reference cell and the preliminarily measured dead volume of the reference cell; and a gas adsorption determining process which comprises the steps of: feeding the gas into a reference volume portion having a known geometric volume with the sample cell and the reference cell being immersed in the cryogenic coolant within the constant temperature bath, and measuring an internal gas pressure of the reference volume portion; allowing the reference volume portion to communicate with the sample cell to introduce the gas from the reference volume portion into the sample cell, and measuring an internal gas pressure of the sample cell; and calculating the amount of the gas adsorbed on the solid sample on the basis of the internal gas pressure of the reference volume portion, the internal gas pressure of the sample cell and the dead volume of the sample cell, wherein the dead volume of the sample cell to be employed for the calculation of the amount of the gas adsorbed on the solid sample is determined in the gas adsorption determining process by measuring an internal gas pressure of the reference cell at a time point of the measurement of the internal gas pressure of the sample cell, and correcting the initial dead pressure of the reference cell and the preliminarily measured dead volume of the reference cell. When the amount of the gas adsorbed on the solid sample is measured, the initial dead volume of the sample cell is corrected on the basis of the internal gas pressure of the reference cell measured at the time point of the measurement of the internal gas pressure of the sample cell, the initial dead volume of the reference cell and the initial internal gas pressure of the reference cell. Then, the corrected dead volume of the sample cell is employed for the calculation of the amount of the gas adsorbed on the solid sample. Therefore, the inventive method obviates the need for performing the troublesome operation for determining the dead volume of the sample cell every time the amount of the gas adsorbed on the solid sample is measured. In addition, there is no need to maintain the environment of the sample cell in a constant state as in the conventional volumetric gas adsorption measuring method. Hence, the amount of the gas adsorbed on the solid sample can easily and accurately be determined.
Where the reference cell has the same inner diameter as a portion of the sample cell which is subjected to a change in the surface level of the cryogenic coolant when being immersed in the cryogenic coolant within the constant temperature bath, a change volume of the sample cell on the basis of the internal gas pressure of the reference cell measured at the time point of the measurement of the internal gas pressure of the sample cell, the initial dead volume of the reference cell and the initial internal gas pressure of the reference cell.
The dead volume of the sample cell is herein defined as the apparent volume of the sample cell excluding the volume of the solid sample on the assumption that the sample cell is entirely maintained at the same temperature as the reference volume portion, and the dead volume of the reference cell is herein defined as the apparent volume of the reference cell on the assumption that the reference cell is entirely maintained at the same temperature as the reference volume portion.
In the gas adsorption measuring method, the dead volume of the reference cell is preliminarily measured and, at this time point, the gas is fed and confined in the reference cell. Then, the initial dead volume of the sample cell and the initial internal gas pressure of the reference cell are measured. The initial dead volume of the reference cell at the time point of the measurement of the initial dead volume of the sample cell is calculated on the basis of the initial internal gas in the dead volume of the reference cell accords with a change in the dead volume of the sample cell. Therefore, the initial dead volume of the sample cell can easily be corrected.
Alternatively, the preparatory process may comprise the steps of: providing, instead of the reference cell, a sensor having a physical property value which is variable proportionally to the change in the surface level of the cryogenic coolant within the constant temperature bath for determination of the dead volume of the sample cell; measuring the initial dead volume of the sample cell and an initial physical property value of the sensor with the sample cell and the sensor being immersed in the cryogenic coolant within the constant temperature bath; and calculating, as a conversion factor, a ratio of a change in the dead volume of the sample cell to the change in the physical property value of the sensor occurring due to the change in the surface level of the cryogenic coolant, wherein the dead volume of the sample cell to be employed for the calculation of the amount of the gas adsorbed on the solid sample is determined in the gas adsorption determining process by measuring a physical property value of the sensor at a time point of the measurement of the internal gas pressure of the sample cell, and correcting the initial dead volume of the sample cell on the basis of the physical property value of the sensor measured at the time point of the measurement of the internal gas pressure of the sample cell, the initial physical property value of the sensor, and the conversion factor. In this method, the amount of the gas adsorbed on the solid sample can easily and accurately be determined.
Alternatively, the preparatory process may comprise the steps of: immersing the sample cell in the cryogenic coolant within the constant temperature bath, and preliminarily determining, as a function of time, the change in the dead volume of the sample cell occurring with time due to lowering of the surface level of the cryogenic coolant within the constant temperature bath; and measuring the initial dead volume of the sample cell with the sample cell being immersed in the cryogenic coolant within the constant temperature bath, wherein the dead volume of the sample cell to be employed for the calculation of the amount of the gas adsorbed on the solid sample is determined in the gas adsorption determining process by determining an amount of the change in the dead volume of the sample cell at the time point of the measurement of the internal gas pressure of the sample cell on the basis of the function according to time elapsed from the time point of the measurement of the initial dead volume of the sample cell, and correcting the initial dead volume of the sample cell on the basis of the amount of the change in the dead volume of the sample cell at the time point of the measurement of the internal gas pressure of the sample cell.
In this method, the change in the dead volume occurring due to the lowering of the surface level of the cryogenic coolant within the constant temperature bath is preliminarily determined as the function of time as described above. When the amount of the gas adsorbed on the solid sample is measured, the initial dead volume of the sample cell previously measured is corrected by determining the amount of the change in the dead volume of the sample cell on the basis of the function according to the time elapsed from the time point of the measurement of the initial dead volume of the sample cell. Therefore, the amount of the gas adsorbed on the solid sample can more efficiently be determined without the need for actually measuring the amount of the change in the dead volume of the sample cell before the determination of the adsorbed gas amount.